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More About Point Spread Functions

Astronomical observations are a funny thing. The image you get cannot be any better than the instrument you are using, and it cannot give you more information than the source itself contains. Most lenses, including all telescopes, are not perfect optical systems. As a result when light rays are passed through the telescope lens the light undergoes a certain degree of degradation. This degradation of a telescope is called its "point spread function" and it serves to limit, in a sense, the information that can be gotten from a telescope. For example, a telescope cannot resolve a point source, like a star. It is too small, and the light that actually comes from a single point in space gets blurred as it passes through the lens of the telescope.

The question is how can this degradation be represented? Well suppose you have an exceedingly small dot of light, a point, and project it through a lens. The image of this point will not be the same as the original. The lens will introduce a small amount of blur. The light from a distant star is just such a dot of light, or "point source." You might think that such a source would appear as a single point in an image, but because of a telescope's point spread function, the image will actually appear to be spread out over many pixels. Different telescopes have different point spread functions, and some have less light distortion. But all telescopes have this property.

ROSAT point spread function
ROSAT image of a point source
Credit: NASA
ASCA point spread function
ASCA image of a point source
Credit: NASA

Shown here are images of point sources that illustrate the point spread function for the ASCA and ROSAT X-ray telescopes. If these were undistorted representations of the star, the stellar image would be smaller than a single pixel of the telescope. Because of the telescope's point spread function, however, the stars appear to be many pixels across, and have a distinct shape. For most stars, because they are so very far away, the point spread function dominates the image, and no characteristics of the star itself can be seen (its shape, for example).

It is possible to remove the distortion caused by a telescope's point spread function (this distortion affects all observations, not just point sources). However, when the point spread function is eliminated, the telescope is still limited by its resolution. Resolution is a telescope's ability to resolve very small objects. For all but the very largest stars, and all but the very most advanced telescopes, the resolution limitations of the telescope mean that the star's angular size is smaller than one pixel of the detector. The one pixel that covers the part of the sky where the star is located will capture all of the star's light (once the effects of the point spread function are removed). The star will appear to be square, because the one pixel is square! All stars of all sizes (but smaller than the telescope's resolution) and the same luminosity will appear to be the same size!

Compare the images above (point source images from different telescopes) to the image of Betelgeuse below. Betelgeuse is a nearby red giant star. Because of its large radius and closeness to Earth, it is not a point source. It is several pixels across in the image from the Hubble Space Telescope below.

HST image of Betelgeuse
Credit: NASA

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